There is a fair bit of debate in Australia at the moment about multi-tasking. It's usually phrased in terms of kids who do their homework, watch TV, SMS and play a game. it's sometimes expressed in terms of women having greater skills than men in doing multiple things at once.
My view is that multi-tasking, at least as normally expressed, is impossible.
To start with a simple example.
Say that I am cooking and listening to the radio. Normally, cooking is a routine task involving physical activity. The mind is not totally engaged, so that I can listen and work. Say, however, that I need to consult a recipe and actually make a decision. The mind is now engaged; the radio drops out.
Alternatively, say that the radio becomes very interesting. The mind is now engaged with it. Cooking will normally slow and even stop.
Another example still involving cooking. Normally in cooking, there are time breaks during which you can watch TV, hang out washing, sort something. At one level, you seem to be multi-tasking in the sense that you seem to be doing two activities or more at once. In practice, you are sequential tasking,
It may seem that those in very busy management roles are multi-tasking. In fact, they become skilled at task shifting and chunking, moving quickly from one task to another.
Leaving aside the tension involved in this, there is a cost where the move from one task to another reduces efficiency. That is why so much management advice centres on ways to increase time available for specific tasks - shut the door, turn off the emails, etc. If we could all multi-task in terms of doing two tasks at once, then this would not be necessary.
One of the difficulties with the discussion on multi-tasking is that is misleads. Not only does it imply that we should somehow be super human, it also confuses thinking about the organisation of work.